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    This module is included inLens: Siyavula: Mathematics (Gr. 7-9)
    By: SiyavulaAs a part of collection: "Mathematics Grade 7"

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Module by: Siyavula Uploaders. E-mail the author

MATHEMATICS

Decimal Fractions

EDUCATOR SECTION

Memorandum

13.4

Table 1
     
a) 2 6010060100 size 12{ { { size 8{"60"} } over { size 8{"100"} } } } {} 2,60
b) 13 62510006251000 size 12{ { { size 8{"625"} } over { size 8{"1000"} } } } {} 13,625
c) 17 7510075100 size 12{ { { size 8{"75"} } over { size 8{"100"} } } } {} 17,75
d) 23 87510008751000 size 12{ { { size 8{"875"} } over { size 8{"1000"} } } } {} 23,875
e) 36 810810 size 12{ { { size 8{8} } over { size 8{"10"} } } } {} 36,8

13.5 a) 0,83

  1. a) 0,2857142
  2. b) 0,8125
  3. c) 0,4

13.6

Table 2
9 2 9 2 size 12{ { { size 8{9} } over { size 8{2} } } } {} 11 2 11 2 size 12{ { { size 8{"11"} } over { size 8{2} } } } {} 325 100 325 100 size 12{ { { size 8{"325"} } over { size 8{"100"} } } } {} 43 5 43 5 size 12{ { { size 8{"43"} } over { size 8{5} } } } {} 201 8 201 8 size 12{ { { size 8{"201"} } over { size 8{8} } } } {} 4056 1000 4056 1000 size 12{ { { size 8{"4056"} } over { size 8{"1000"} } } } {} 199 5 199 5 size 12{ { { size 8{"199"} } over { size 8{5} } } } {}
4 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {} 5 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {} 3 2510025100 size 12{ { { size 8{"25"} } over { size 8{"100"} } } } {} 8 3535 size 12{ { { size 8{3} } over { size 8{5} } } } {} 25 1818 size 12{ { { size 8{1} } over { size 8{8} } } } {} 4 561000561000 size 12{ { { size 8{"56"} } over { size 8{"1000"} } } } {} 39 4545 size 12{ { { size 8{4} } over { size 8{5} } } } {}
4,5 5,5 3,25 8,6 25,125 4,056 39,8

14. a) 0,3

  1. a) 0,6
  2. b) 0,23

Leaner Section

Content

ACTIVITY: More revision [LO 1.4.2, LO 1.10, LO 2.3.1, LO 2.3.3]

We can convert proper fractions to decimal fractions in this way:

Figure 1
Figure 1 (graphics1.png)

13.2 Did you know?

We can also calculate it in this way:

Figure 2
Figure 2 (graphics2.png)

13.3 Which of the methods shown above do you choose?

Why?

13.4 Complete the following tables:

Figure 3
Figure 3 (graphics3.png)

13.5 Use the division method as shown in 13.2 and write the following fractions as decimal fractions:

a) 5656 size 12{ { {5} over {6} } } {} ........................................................................... ...........................................................................

...........................................................................

b) 2727 size 12{ { {2} over {7} } } {} ........................................................................... ...........................................................................

...........................................................................

c) 13161316 size 12{ { {"13"} over {"16"} } } {} ........................................................................... ...........................................................................

...........................................................................

d) 4949 size 12{ { {4} over {9} } } {} ........................................................................... ...........................................................................

...........................................................................

13.6 Can you complete the following table??

Table 3
Improper fraction 9 2 9 2 size 12{ { { size 8{9} } over { size 8{2} } } } {}     45 5 45 5 size 12{ { { size 8{"45"} } over { size 8{5} } } } {}      
Mixed Number   5 1 2 5 1 2 size 12{5 { { size 8{1} } over { size 8{2} } } } {}     25 1 8 25 1 8 size 12{"25" { { size 8{1} } over { size 8{8} } } } {}   39 4 5 39 4 5 size 12{"39" { { size 8{4} } over { size 8{5} } } } {}
Decimal fraction     3,25     4,056  

14. BRAIN-TEASERS!

Write the following fractions as decimal fractions. Try to do these sums first without a calculator!

a) 1313 size 12{ { {1} over {3} } } {} ........................................................................... ...........................................................................

...........................................................................

b) 2323 size 12{ { {2} over {3} } } {} ........................................................................... ...........................................................................

...........................................................................

c) 23992399 size 12{ { {"23"} over {"99"} } } {} ........................................................................... ...........................................................................

...........................................................................

15. Do you still remember?

We call 0,666666666 . . . a recurring decimal. We write it as 0,60,6 size 12{0, {6} cSup { size 8{ cdot } } } {}.

0,454545 . . . is also a recurring decimal and we write it as 0,450,45 size 12{0, {4} cSup { size 8{ cdot } } {5} cSup { size 8{ cdot } } } {}.

We normally round off these recurring decimals to the first or second decimal place, e.g.: 0,60,6 size 12{0, {6} cSup { size 8{ cdot } } } {} becomes 0,7 or 0,67 and 0,450,45 size 12{0, {4} cSup { size 8{ cdot } } {5} cSup { size 8{ cdot } } } {} becomes 0,5 or 0,45

16. Time for self-assessment

Table 4
  • Tick the applicable block:
 YES NO  
I can:      
Compare decimal fractions with each other and put them in the correct sequence.      
Fill in the correct relationship signs.      
Round off decimal fractions correctly to:      
  • the nearest whole number
      
  • one decimal place
      
  • two decimal places
      
  • three decimal places
      
Convert fractions and improper fractions correctly to decimal fractions.      
Explain what a recurring decimal is.      

Assessment

Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment Standard 1.4: We know this when the learner recognises and uses equivalent forms of the rational numbers listed above, including:

1.4.2 decimals;

Assessment Standard 1.10: We know this when the learner uses a range of strategies to check solutions and judges the reasonableness of solutions.

Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment Standard 2.3: We know this when the learner represents and uses relationships between variables in a variety of ways using:

2.3.1 verbal descriptions;

2.3.3 tables.

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